The 59-year-old actor has infuriated the president with his impersonation of him on 'Saturday Night Live' but finds the fact the US leader has the time to attack him on social media while running the country to be bizarre.

He said: ''It is kind of surreal, the President of the US.

''I said to somebody, 'Does he have alerts or does he sequester himself for a period of tweeting?'''

Alec went on to muse on how he thinks the former 'Apprentice' star finds the time to lash out on Twitter.

Speaking to Jimmy Fallon, he continued: ''Watching 'Fox and Friends' in the morning, he's got a triple order of bacon, apparently he loves bacon, he eats lots of bacon, and he's got his phone and watches the news in his boxers, tweeting, tweeting.

''Or does he get alerts, he's in a session with like North Korean diplomats and then he's like, 'Hold on a minute please, Alec Baldwin - loser. Horrible movies, mediocre career.'

''Does he tweet throughout the day? Or is it a big binge thing, like a camel at an Oasis, drinks a big long drink in the morning and then goes off.''

And the 'Match Game' host admitted his portrayals of the president can be ''exhausting'', especially as he never expected to be playing him for so long.

He said: ''Everybody knows that ['SNL' producer Lorne Michaels] came to me and I thought we were going to do it for three weeks in the fall.

''Then he won, and I was in bed like, 'Oh, no.'

''I don't need to tell you, it gets exhausting.''

Earlier this month, the president slammed Alec on Twitter after he said his impressions were ''agony''.

He wrote: ''Alec Baldwin, whose dying mediocre career was saved by his terrible impersonation of me on SNL, now says playing me was agony. Alec, it was agony for those who were forced to watch. Bring back Darrell Hammond, funnier and a far greater talent! (sic)''

But the '30 Rock' star quickly hit back.

He responded: ''Agony though it may be, I'd like to hang in there for the impeachment hearings, the resignation speech, the farewell helicopter ride to Mara-A-Lago. You know. The Good Stuff. That we've all been waiting for.(sic)''